Method for indicating optical performance of spectacle lens

ABSTRACT

A method for displaying an optical performance preferably applicable to also an axially asymmetric spectacle lens is provided. First, a clear visual region of the spectacle lens is determined using an evaluation function which evaluates the optical performance of the spectacle lens. Next, a clear visual angle which depends on a size of the clear visual region corresponding to a vertex angle of a spherical cone is calculated when the spherical cone which has an equal solid angle with a solid angle including the determined clear visual region from a center of rotation of an eye and which is symmetrical to an optical axis of the spectacle lens is assumed. Next, the calculated clear visual angle is expressed by a unit of degree.

TECHNICAL FIELD

The present invention relates to a method for displaying opticalperformances of a spectacle lens, and more particularly to a method fordisplaying the optical performances suitable for a comparison of anaxially asymmetric lens, lenses having different diameters, or the like.

BACKGROUND ART

As a general method for displaying optical performances of a lens, forexample, a method described in Patent Document 1 is known. In thismethod, first, a predetermined sectional direction in a refractivesurface of the lens is specified. After this, two evaluation indicatorsas an astigmatism and a power error (curvature of field) are used as theoptical performances in the sectional direction, and are displayed onone longitudinal aberration graph. The longitudinal aberration graph isa graph which displays longitudinal aberration of the lens along ameridian. The method for displaying the optical performances of the lensby the longitudinal aberration graph is preferably used for evaluationof an axially symmetrical lens such as a camera lens or the like, or aspectacle lens.

Patent Document 1: Japanese Patent Laid-open No. Sho 58-24112

However, some spectacle lenses such as a single vision aspherical lens,an astigmatic lens, a progressive-power lens, or the like are notaxially symmetrical. When the optical performances of the spectaclelenses which are not axially symmetrical are displayed on thelongitudinal aberration graph, only the optical performances in aspecified direction along the meridian can be seen. Therefore, theoptical performances of an entire axially asymmetric spectacle lens arenot fully evaluated. Incidentally, it is also thought that an aberrationgraph along a direction other than the meridian can be prepared anddisplayed; however, such an aberration graph is not realistic because itis numerously required and hard to understand.

Furthermore, in the aforementioned display method, when the longitudinalaberration graphs of two different lenses are compared, especially whendiameters of these lenses are different, there is a problem that it isdifficult to quantitatively compare the optical performances as theentire lenses.

Moreover, in the aforementioned display method, there is a problem thatthose who do not have technical knowledge of the lens do notinstinctively grasp the optical performances of the lens from thelongitudinal aberration graphs.

An object of the present invention is to provide a method for displayingoptical performances preferably applicable to also the axiallyasymmetric spectacle lens. Furthermore, an object of the presentinvention is to appropriately and easily conduct a comparison of theoptical performances of the lenses having different design conditionssuch as the diameter or the like. Furthermore, an object of the presentinvention is to quantitatively evaluate the optical performances as theentire lens. Furthermore, an object of the present invention is todisplay the optical performances of the spectacle lens also for thosewho do not have the technical knowledge to instinctively and easilyunderstand.

DISCLOSURE OF THE INVENTION

The present invention is a method for displaying an optical performanceof a spectacle lens, comprises: determining a clear visual region of thespectacle lens; calculating an optical performance value which dependson a size of the clear visual region capable of calculating based on aspherical cone when the spherical cone which has an equal solid anglewith a solid angle including the determined clear visual region from acenter of rotation of an eye and which is symmetrical to an optical axisof the spectacle lens is assumed; and displaying the optical performanceof the spectacle lens using the calculated optical performance value.Respective steps are explained in detail hereinafter.

[Determining Clear Visual Region]

First, the clear visual region of the spectacle lens is determined. Theclear visual region is a region of the spectacle lens which can beclearly (clear) seen. This term can be expressed by replacing adifferent term such as, for example, a distinct visual region or astandard visual region, and not terminologically limited. Whendetermining the clear visual region, indicators such as astigmatism, apower error (mean power error), distortion aberration, a tangentialerror, a sagittal error, or the like can be used as a reference,however, an evaluation function about visual acuity of the spectaclelens is preferably used. Here, the evaluation function about the visualacuity is a function to calculate optical performance values about thevisual acuity in each evaluation point which is set up on the spectaclelens.

Specifically, a range of a converted visual acuity value (to bedescribed later) which defines the clear visual region can be preferablyset up within a range of zero to 0.1 or 0.2 expressed by a [logMAR] unitwhen zero is defined as the clearest. This range is expressed as about0.6 to about 0.8 by decimal visual acuity. This range is a preferablereference value which can be evaluated as a visual acuity value by acommon sense. However, the range of the converted visual acuity valuewhich defines the clear visual region is not specially limited.

As the evaluation function about the visual acuity, there are convertedvisual acuity to be described later, visual acuity V (refer to claim 4of Japanese Patent Laid-open No. Sho 58-24112), RMS, or the like. RMS isa spread of points where a group of rays which transmit the spectaclelens so as to make a focus crosses a plane which passes through thefocal point and which is perpendicular to an optical axis of thespectacle lens. The respective points can be displayed by a point spreadfunction.

Incidentally, the evaluation function is preferably obtained from designdata of the spectacle lens; however, it can be obtained also from dataof measured values or the like.

A different aberration according to a distance (for example,respectively near and far) of an object through the spectacle lens isgenerated in the spectacle lens. Therefore, the evaluation function ofthe single visual acuity depending on the distance of the object ispreferable. Specifically, for example, converted visual acuity isadopted as a single evaluation function about the visual acuity. Here, acalculation of the converted visual acuity is explained hereinafter.

In regards to improvement of the visual acuity, it is important toconsider not only the optical performances of the spectacle lens itselfbut also processing of a retina and a brain. As a paper on the visualacuity and the processing of the retina and the brain, OptmetricMonthly, Nov.: 31-32, 1981: written by Robert N. Kleinstein(hereinafter, referred to as Paper 1) is available. In Paper 1, anexperiment of measuring visual acuity of a subject who constantly wearsspectacles with his/her spectacles taken off is described. Measurementresults are also shown in a view in which a visual acuity measured valueis expressed by a fraction visual acuity value, taking spherical diopter(S diopter) and cylindrical diopter (C diopter) in a horizontal axis anda vertical axis respectively. The same view as this view is shown inFIG. 4. Incidentally, the S diopter and the C diopter are used asspectacle terms by those in the art.

In order to use the measured values of Paper 1 as the evaluationfunction, the measured values are modified in such a manner that thesigns of the horizontal axis value S and the vertical axis value C inPaper 1 are reversed, namely, residual S diopter and residual C diopterare taken in the horizontal axis and the vertical axis respectively.Thus, the modified data are equivalent to evaluation data showing howthe visual acuity decreases when a subject having normal visual acuitywears spectacles with aberration, reversely to the experiment in Paper1.

Incidentally, in Paper 1, data of spectacle wearers for the age of 5 to15, 25 to 35, and 45to 55are described as experimental data, however, itis preferable to use a virtual visual acuity measured value not affectedby an adjusting power of the eyes (a unit is diopter). Therefore, thedata for the age of 45 to 55 are used from Paper 1 for convenience sake,and improved; thereby the aforementioned evaluation data are obtained.

Here, the residual S diopter and the residual C diopter are correlatedto an astigmatism and a curvature of field as described later. IfListing's Law is not taken into consideration, however, the astigmatismand the curvature of field cannot be calculated accurately in regions inwhich an eyeball does not rotate along two lens principal meridians.Here, the Listing's Law means that there is a rotation axis of aneyeball motion in a plane (Listing's surface) which is perpendicular toan eye position and which includes a center of rotation of an eyeballwhen the eyeball looks far forward (first eye position).

In other words, on an axis in a lens radiation direction other than theS and C axes of an astigmatic lens, it is necessary to calculate theastigmatism and the curvature of field with the eyeball motion takeninto consideration. Therefore, a calculation of a new aberration (theastigmatism and the curvature of field) in which the Listing's Law istaken into consideration is performed in order to use the visual acuitymeasured value in Paper 1 as an evaluation function on an entire surfaceof a lens.

Hereinafter, the correlation of the residual S diopter and the residualC diopter with the astigmatism and the curvature of field in which theListing's Law is taken into consideration will be explained. Taking theListing's Law into consideration, when the eyeball rotates in adifferent direction from the principal meridians of the spectacle lens,the angle between the principal meridians and coordinate axes rotatingaccording to the Listing's Law does not become 0 (zero). Accordingly,when an angle deviation described in, for example, Japanese PatentLaid-open No. Sho 57-10112 (hereinafter, referred to as Paper 2) occurs,the following typical problems arise.

In other words, even when a value of the astigmatism is equal with anabsolute value of a reference astigmatism (an astigmatic amount and acylinder axis at the center of a lens), the astigmatism is a vectorvalue having a direction so that a residual astigmatism whose value isnot 0 (zero) is newly generated. It should be noted that, as for acalculation of the residual astigmatism, methods for calculating anastigmatic lens and the residual astigmatism of the astigmatic lens asdisclosed in Paper 2 or the like are applicable.

Meanwhile, the curvature of field as another factor does not change dueto the coordinate change according to the Listing's Law since thecurvature of field is a scalar value, not the vector value.

Based on the above, the correlation of the residual astigmatism and thecurvature of field with the residual S diopter and the residual Cdiopter is as follows:

(1) When the residual astigmatism is positive, their correlation isexpressed by the following equations (a), (b):residual S diopter=curvature of field−residual astigmatism/2  (a)residual C diopter=residual astigmatism  (b)

(2) When the residual astigmatism becomes negative in an opticalcalculation, their correlation is expressed by the following equations(c), (d) based on an idea similar to diopter conversion of spectaclessince the residual C diopter is defined as positive:residual S diopter=curvature of field+residual astigmatism/2  (c)residual C diopter=−residual astigmatism  (d)

Next, when seeing FIG. 4, it is first found out that a value of thehorizontal axis (residual S diopter) is not symmetrical with respect tothe origin. Furthermore, a value of the vertical axis (residual Cdiopter) has also nonlinear data peculiar to a living human body. Forexample, when visual acuity values with the same absolute value on thehorizontal axis and with different signs are examined, it is clear thata functional relation is not simple. In other words, the visual acuityvalue is nonlinear relative to the optical performance value.Accordingly, the nonlinear nature peculiar to the living human bodyneeds to be taken into consideration.

Therefore, in the present invention, an interpolation function V isfirst calculated from the data on the visual acuity measured values inFIG. 4. Specifically, the visual acuity values for horizontal axisvalues (residual S diopter) and vertical axis values (residual Cdiopter) are respectively scaled for 0.1 to 1 diopter, and the visualacuity values are discretely plotted. Then, by interpolating the visualacuity values on the plane coordinate using a generally knowninterpolation method, the interpolation function V including residual Sdiopter and residual C diopter as variable factors is calculated. Theinterpolation function V is expressed by the following equation:interpolation function V=V (residual S diopter, residual C diopter)  (e)

According to the equation (e), the interpolation function V can becalculated even when the residual S diopter and the residual C diopteras the variable factors are a continuous value, not a discrete value.

When calculated results of the equations (a), (b) or the equations (c),(d) are respectively substituted with the residual S diopter and theresidual C diopter as the variable factors in the equation (e), thefollowing equation (f) is obtained.interpolation function V=V (curvature of field, residualastigmatism)  (f)

In the equation (f), a right side is obtained by the optical calculationand a left side is the visual acuity value by actual measurement. Theoptical value and the visual acuity value are thus correlated.

The interpolation function V in the equation (f) can be used as anevaluation function in this state. However, since nonlinearity is high,it is hard to say that it is the best state for an optimizationcalculation. Therefore, it is further transformed to the followingequation (g) expressed by a visual acuity evaluation function (convertedvisual acuity), which is a definition equation for representing visualacuity. A unit of a value of the converted visual acuity according tothe equation (g) is [logMAR].converted visual acuity[logMAR]=log₁₀(1/V(curvature of field, residualastigmatism))  (g)

Through the above processes, the converted visual acuity in which thenonlinear nature is taken into consideration is derived from the opticalperformance of the living human body. The visual acuity of the livinghuman body of course changes depending on age, a measurementenvironment, and so forth. In fact, however, the above-described basicmethod requires a large calculation amount in the optimizationcalculation. Therefore, instead of the equation (e), approximateequations such as the following equations (h), (I) can be used:V′=2^(−X·K)  (h)where, K is expressed by the following equation (I):K=[(residual S diopter+residual C diopter/2)²+(residual Cdiopter/2)²]^(1/2)  (I)

where, X is a value within a range of 0.5 to 2, and is determined byactual measured data. For example, X=1.442695 according tolog₁₀e=1.442695×log₁₀2, or the like.

The interpolation function V′ in the equation (h) may be used as theevaluation function in this state. The correlation with the convertedvisual acuity [logMAR] is expressed by the following equation (j), asexplained in the aforementioned basic method.converted visual acuity[logMAR]=X×log₁₀2×{(curvature of field²+(residualastigmatism/2)²}^(1/2)   (j)

Here, the curvature of field is aberration in an evaluation point of thespectacle lens, and aberration also referred to as a mean power error, apower error, an MOE or the like. The residual astigmatism is anastigmatism considering the Listing's Law.

The evaluation point is plural virtual points which are set up on thespectacle lens in order to evaluate the optical performances of thespectacle lens. When the respective evaluation points are set up, thestate in which a ray passes the spectacle lens is assumed and a raytracing method or the like is used. About 5 to 10 evaluation points onan axially symmetrical lens can be set up and about 15 to 10000evaluation points can be set up on an axially asymmetric lens. Then,values of the evaluation function (converted visual acuity) in therespective evaluation points are calculated.

The aforementioned equation (j) is an equation in which the opticalvalue and the visual acuity value are correlated. Furthermore, theapproximate equation can be transformed by adding measured values byages in addition to actual visual acuity data or by using another visualacuity measurement data.

It should be noted that an equation of a general regular spherical lensor the like in which Listing's Law is not considered is as follows:converted visual acuity[logMAR]=X×log₁₀2×{curvature offield²+(astigmatism/2)²}^(1/2)  (k).The astigmatism in the equation (k) represents astigmatism in which theListing's Law is not considered. The equation (k) can also be used asthe converted visual acuity.

If the converted visual acuity according to the equation (j) or theequation (k) is used, an optical value (astigmatism, curvature of field,distortion aberration) of the spectacle lens can be transformed to theconverted visual acuity and displayed regardless of a sphere, anaspheric surface, an astigmatic lens, a progressive-power lens.

Furthermore, the following equation can be defined by using theabove-explained converted visual acuity.

$\begin{matrix}\left\lbrack {{Equation}\mspace{14mu} 4} \right\rbrack \\{{{{merit}\mspace{14mu}{function}} = {{a \times {\sum\limits_{n}\left( {{u_{n}\; \cdot {far}}\mspace{14mu}{vision}\mspace{14mu}\log\;{MAR}_{n}} \right)^{2}}} + \mspace{185mu}(L)}}\mspace{76mu}{\quad{{b \times {\sum\limits_{n}\left( {{v_{n} \cdot {near}}\mspace{14mu}{vision}\mspace{14mu}\log\;{MAR}_{n}} \right)^{2}}} + {c \times {\sum\limits_{n}\left( {{w_{n} \cdot {residual}}\mspace{14mu}{DIST}_{n}} \right)}}}}}\end{matrix}$

Here, a, b, c are weight distribution of the respective converted visualacuity (evaluation functions); u_(n), v_(n), w_(n) are weightdistribution at each evaluation point; and n is an evaluation point.Incidentally, an idea that weight is 0 (zero) is included. However,here, 0 (zero) is not adopted as the weight.

In the equation (L), far vision logMAR is converted visual acuity in thefar vision, and near vision logMAR is converted visual acuity in thenear vision. Here, the far vision can be arbitrarily andterminologically defined to a certain extent; however, for example, itcan be defined as a range from a reference point to 10 [m] or infinitybased on a common sense. This range is expressed as 0 (zero) [D] or 0.1[D] by a diopter unit. Also, the near vision is similarly defined as thefar vision, for example, within a range from the reference point to 30[cm] or 33 [cm]. This range is expressed as approximately 3 [D] or 3.33[D] by a diopter unit.

There is no uniform standard where the reference point is determined;however, generally, it is any one of a center of rotation of the eye, alens surface, or a center of a cornea.

Also in the equation (L), residual DIST is the residual astigmatism ofthe spectacle lens, and calculated by the following equation (m).residual DIST=Sign×100×(|residual visual angle magnification|/|centralvisual angle magnification M ₀|)  (m)

In the equation (m), the residual visual angle magnification isexpressed as follows:residual visual angle magnification=peripheral visual anglemagnification M−central visual angle magnification M ₀where,central visual angle magnification M0=lim_(exit angle→0)(tan(exitangle)/tan(incident angle))peripheral visual angle magnification M=tan(exit angle)/tan(incidentangle)(refer to KOHGAKU (OPTICS), Vol. 19, No. 10 “Futatabi Kakubairitsunitsuite (On Angle Magnification Again)” written by Kazuo Miyake, et.al.).

Furthermore, the residual DIST is generally a vector and the Sign showsa direction thereof.

According to the aforementioned equation (L), by choosing the weightdistribution as an appropriate value, a final vision through thespectacle lens can be expressed more faithfully. Especially, ondesigning the spectacle lens, a function defined by combining theconverted visual acuity (evaluation function) as in the equation (L) iscalled a merit function. The clear visual region can also be defined bythe merit function (evaluation function).

Meanwhile, the values of the converted visual acuity in all evaluationpoints which are set up on the spectacle lens are calculated using theaforementioned evaluation function (converted visual acuity). Then, theevaluation points where all calculated results thereof are within apredetermined range are specified, and a region including a group of thespecified evaluation points is determined as a clear visual region.Incidentally, as the converted visual acuity, the equation (j) in whichthe Listing's Law is taken into consideration is preferably used.

[Comparison Art]

Here, a display method previously devised by the inventors is explainedfor comparison with the present invention. A clearly seen region within,for example, the converted visual acuity of 0.1 [logMAR] is defined asthe clear visual region, and a ratio of a size of the clear visualregion to clear visual region ratio P (%) and expressed by percent usingthe following equation (n).first clear visual region ratio P(%)=100×A/B  (n)

where, B is a solid angle [steradian] extending from a center ofrotation of the eyeball to the entire spectacle lens, and A is a solidangle [steradian] extending the clear visual region of the spectaclelens.

A concrete calculation method of the equation (n) is calculated by thefollowing equation (O) equivalent to the equation (n). The number K ofmany (mathematically) random rays is generated from the center ofrotation of the eyeball to a front hemisphere by the ray tracing method,and the number of rays which transmit the entire lens is considered asBd, and the number thereof which transmit the clear visual region isconsidered as Ad. In this case, A and Ad, B and Bd respectively haveproportional relations. Accordingly, a second clear visual region ratiois calculated by the following equation (O).

$\begin{matrix}\left\lbrack {{Equation}\mspace{14mu} 5} \right\rbrack & \; \\{{{second}\mspace{14mu}{clear}\mspace{14mu}{visual}\mspace{14mu}{region}\mspace{14mu}{ratio}\mspace{14mu}{P(\%)}} = {100 \times {\lim\limits_{K\rightarrow\infty}\frac{Ad}{Bd}}}} & (O)\end{matrix}$

Furthermore, instead of the equation (O), the clear visual region ratiocan be approximately calculated by also the following equation (p) as athird clear visual region ratio. The reason to use a term“approximately” is because the proportional relation between the numberof rays and the solid angles is broken when a visual angle is large.However, since the solid angle is small within a range of a general lensdiameter (a diameter of 80 [mm] or less), the equation (p) is usablewith no problem.

When the rays enter from the center of rotation of the eyeball to thelens with the same intervals, the equation (p) is made up as a followingthird clear visual region ratio.

$\begin{matrix}\left\lbrack {{Equation}\mspace{14mu} 6} \right\rbrack & \; \\{{{third}\mspace{14mu}{clear}\mspace{14mu}{visual}\mspace{14mu}{region}\mspace{14mu}{ratio}\mspace{14mu}{P(\%)}} = {100 \times {\lim\limits_{K\rightarrow\infty}\frac{N}{Be}}}} & (p)\end{matrix}$

where, B_(e) is the number of rays which transmit the entire spectaclelens, and N is the number thereof which transmit the clear visualregion.

According to an expression by percent in the clear visual region ratiousing the aforementioned equations from (n) to (p), a size of the clearvisual region is instinctively easy to understand. On the other hand,when the entire spectacle lens changes (for example, change of a lensdiameter), the solid angle B changes even if the aforementioned clearvisual region ratio P% has the equal solid angle A. Furthermore, anexpression by the aforementioned solid angle A is a theoreticallyaccurate expression, but it is instinctively hard to understand as anexpression of the spectacle lens. Furthermore, the solid angle extendingin the clear visual region is not symmetrical to the optical axis whenthe spectacle lens is not symmetrical to the optical axis. Therefore,this method has a room to consider when the optical performances havinglenses of different diameters are compared.

[Calculating Optical Performance Value]

Therefore, in the present invention, an optical performance value whichdepends on a size of the clear visual region capable of calculatingbased on a spherical cone is more preferably calculated when thespherical cone which has an equal solid angle with a solid angleincluding the determined clear visual region from the center of rotationof the eye (center of rotation of the eyeball) and which is symmetricalto the optical axis of the spectacle lens is assumed. The calculation ofthe optical performance value includes a calculation of a clear visualangle and a calculation of a clear visual diameter, both of which aredescribed later.

Incidentally in an embodiment of the invention, a range within 0.1[logMR] by converted visual acuity is defined as the clear visualregion.

(a) Calculating clear visual angle

First, the solid angle [steradian] is calculated as a spherical cone 6symmetrical to an optical axis 4 of a spectacle lens 2 as shown inFIG. 1. The spherical cone 6 has a center of rotation of eyeball 12 as avertex and has a spherical portion on a side of the spectacle lens 2.

If a vertex angle θ of the spherical cone 6 is calculated and expressedby a unit of degree as the clear visual angle, it is a form ofexpression easy to understand. The vertex angle θ of the spherical cone6 is a vertex angle θ when the spherical cone 6 is cut in a flat surfaceincluding the optical axis 4. It should be noted that a term clearvisual angle is coined by the inventors, and it can be replaced as, forexample, an average visual angle or an equivalent visual angle.

Specifically, the clear visual angle can be calculated by the followingequation (q) (first clear visual angle).

$\begin{matrix}\left\lbrack {{Equation}\mspace{14mu} 7} \right\rbrack & \; \\{{{first}\mspace{14mu}{clear}\mspace{14mu}{visual}\mspace{14mu}{angle}} = {\lim\limits_{K\rightarrow\infty}{2 \times {\cos^{- 1}\left( {1 - \frac{Ad}{K}} \right)}}}} & (q)\end{matrix}$

where, K is the number of rays when many rays (mathematically) randomlyenter the front hemisphere of the spectacle lens, and Ad is the numberof the rays which transmit the clear visual region among the rays.

Furthermore, the front hemisphere of the spectacle lens means a frontsolid angle (a value is 2×π steradian).

As a concrete calculation of the equation (q), a spherical cone of aunit sphere symmetrical to the optical axis 4 having a center ofrotation of eyeball 12 as a vertex is thought. An angle made by thespherical cone is the clear visual angle. If the solid anglecorresponding to the number Ad of rays is considered as an area of aspherical portion of the aforementioned spherical cone, the solid anglecorresponding to the number K of rays, being 2×πhas the followingrelationship.

[Equation  8]${{Ad}:K} = {{2 \times \pi \times \left\lbrack {1 - {\cos\left( \frac{{first}\mspace{14mu}{clear}\mspace{14mu}{visual}\mspace{14mu}{angle}}{2} \right)}} \right\rbrack}:{2 \times \pi}}$

The equation (q) is made up by the above equation.

Furthermore, instead of the equation (q), the clear visual angle can beapproximately calculated by also the following equation (r) as a secondclear visual angle. The reason to use a term “approximately” is becausethe proportional relation between the number of rays and the solidangles is broken when the visual angle is large. However, since thesolid angle to the spectacle lens having a lens diameter (specifically,for example, a diameter of 80 [mm] or less) used in a general spectaclesindustry is small, the following equation (r) can be used with noproblem because the aforementioned proportional relation does notpractically affect a lens.

$\begin{matrix}\left\lbrack {{Equation}\mspace{14mu} 9} \right\rbrack & \; \\{{{second}\mspace{14mu}{clear}\mspace{14mu}{visual}\mspace{14mu}{angle}} \cong {2 \times L \times \sqrt{\frac{N}{\pi}}}} & (r)\end{matrix}$

where, L is a degree interval when many rays enter from the center ofrotation of eyeball 12 to the spectacle lens 2 with same degreeintervals (for example, 1° pitch), and N is the number of rays whichtransmit the clear visual region among incident rays.

The value of the clear visual angle calculated as above is a value whichdepends on an absolute size of the clear visual region of the spectaclelens 2, not on the lens diameter. The value of the clear visual anglecan be used as the optical performance value of the spectacle lens 2.

(b) Calculating clear visual diameter

In this step, a value of a clear visual diameter R corresponding to adiameter R of a circle obtained by projecting the solid angle of thespherical cone 6 on a flat surface 10 which is perpendicular to theoptical axis 4 and which includes a rear vertex 8 of the spectacle lens2 is calculated.

Specifically, the flat surface 10 in FIG. 1 which is perpendicular tothe optical axis 4 and which includes the vertex (the rear vertex) 8 ona rear surface 2 b of the lens 2 is considered as a rear flat surface.If the solid angle of a shape of the spherical cone 6 is projected onthe rear flat surface 10, a circle appears on the rear flat surface 10.An outside diameter R of the circle is considered as a clear visualdiameter (an equivalent diameter or an average diameter) of the clearvisual region. The clear visual diameter R can be approximatelycalculated using the following equation (s) based on the clear visualangle (the equivalent visual angle) θ and a value of a distance VRbetween the rear vertex 8 and the center of rotation of eyeball 12.Incidentally, a term clear visual diameter is coined by the inventors.

$\begin{matrix}\left\lbrack {{Equation}\mspace{14mu} 10} \right\rbrack & \; \\{{{clear}\mspace{14mu}{visual}\mspace{14mu}{diameter}} = {2 \times {VR} \times {\tan\left( \frac{{clear}\mspace{14mu}{visual}\mspace{14mu}{angle}}{2} \right)}}} & (s)\end{matrix}$

The clear visual angle θ or the clear visual diameter R of the clearvisual region is easy to understand because even the spectacle lenseshaving different outside diameters and refractive indexes can be treatedwith a same sense.

It should be noted that a value calculated by the aforementionedequation (q) or equation (r) can be substituted with the clear visualangle θ in the equation (s).

Incidentally, in FIG. 1, a point where a ray generated at the angle ofη/2 [degree] from the center of rotation of eyeball 12 to the opticalaxis 4 crosses a lens front surface 2 a is considered as P1, and a valuethat a distance between the point P1 and the optical axis 4 is doubledis considered as K1. Also, in FIG. 1, when a line perpendicular to aconnecting point of the outside diameter on the optical axis 4 of thespectacle lens 2 in a vertical direction is thought, a point where theperpendicular line crosses a ray of an extended line of the point P1 isconsidered as P2, and a value that a distance between the point P2 andthe optical axis 4 is doubled is considered as K2. In this case, thesmaller value of K1 or K2 can be defined as the clear visual diameter.However, in this case, a spectacle lens asymmetric to the optical axis 4often has a case that the clear visual diameter changes according toevery azimuth of the lens so as to become an axially asymmetricdiameter, or that the clear visual diameter similarly changes due todesign of a center thickness of the lens. Therefore, the clear visualdiameter approximately calculated using the equation (s) is preferable.

The value of the clear visual diameter calculated as above depends on anabsolute size of the clear visual region of the spectacle lens 2 and isnot affected by the lens diameter. Therefore, the value of the clearvisual diameter can be preferably used as the optical performance valueof the spectacle lens 2.

Hitherto, a calculation method of the clear visual angle and the clearvisual diameter which depend on the size of the clear visual region isexplained. Incidentally, the clear visual angle and the clear visualdiameter can be similarly calculated by measuring the clear visualregion and using the measurement results thereof. The clear visualregion can be directly measured to human eyes or mechanically measuredby a measuring instrument. Specifically, the clear visual region ismeasured from the center of rotation of eyeball 12 with a same degreeinterval L [°] and the number of N which can be seen clearly ismeasured. Then, the clear visual diameter and the clear visual angle arecalculated using the equations (s), (r).

Furthermore, the measuring instrument which directly measures the clearvisual region by a steradian unit can calculate the clear visual angleby the following equation (t).clear visual angle=2×COS⁻¹(1−A/2π)  (t)

where, A is the clear visual region and A steradian. The clear visualdiameter is measured by the equation (s).

Furthermore, 0.1 or below by the [logMAR] unit is considered as theclear visual region, and needless to say that, for example, 0.2 or belowcan be treated as the clear visual region and processed using theequations (n) or after.

[Displaying Optical Performance]

Next, the optical performances of the spectacle lens are displayed byusing the calculated optical performance value. According to a preferredembodiment, the calculated value of the clear visual angle by thecalculation of the clear visual angle is expressed by a unit of degree(for example, degree [°] or radian [rad]) as the optical performancevalue. Also, according to another preferred embodiment, the calculatedvalue of the clear visual diameter by the calculation of the clearvisual diameter is expressed by a unit of length (for example, [mm]) asthe optical performance value.

The display described here includes all of the display of the opticalperformance value corresponding to plural lenses as a chart or a graph,displaying an image according to the optical performance value, and thelike in addition to expressing the optical performance value describedabove.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is an explanatory view of a clear visual angle and a clear visualdiameter;

FIG. 2 is a view three-dimensionally showing values of an evaluationfunction on astigmatic lenses for explaining design conditions of theastigmatic lenses as display objects of optical performances in anexample. FIGS. 2A and 2B respectively correspond to astigmatic lenseshaving diameters of 80 [mm] and 70 [mm];

FIG. 3 is a view three-dimensionally showing values of an evaluationfunction on astigmatic lenses for explaining design conditions of theastigmatic lenses as display objects of optical performances in anotherexample. FIGS. 3A and 3B respectively correspond to astigmatic lenseshaving diameters of 80 [mm] and 60 [mm]; and

FIG. 4 is a view showing measurement results of visual acuity shown inreferences.

2 . . . spectacle lens, 4 . . . optical axis, 6 . . . spherical cone, 8. . . rear vertex, 10 . . . rear flat surface (flat surface), 12 . . .center of rotation of eyeball (center of rotation of the eye), θ . . .clear visual angle, R clear visual diameter, VR . . . distance betweenrear vertex and center of rotation of eyeball.

BEST MODE FOR CARRYING OUT THE INVENTION EXAMPLE 1

Optical performances of two astigmatic lenses respectively havingdiameters of 80 [mm] and 70 [mm] are calculated. Common lens data ofboth are listed in Table 1.

TABLE 1 Spherical diopter (D) −4 Cylindrical diopter (D) −2 Refractiveindex 1.60 Center thickness (mm) 1 Front surface curvature (1/mm)0.00535610067114 Rear surface curvature (sphere) 0.01207824453097 (1/mm)Rear surface curvature (astigmatism) 0.01375609687996 (1/mm)

Furthermore, the distances VR between the rear vertexes 8 and thecenters of rotation of eyeball 12 of both the astigmatic lenses are28.333 [mm].

FIG. 2 is a view three-dimensionally displaying the optical performancesof the lenses for explaining actual sizes or shapes of clear visualregions in the astigmatic lenses. In this drawing, visual angles aretaken in horizontal axes, and scaled for every two [degree] pitch.Converted visual acuity values [logMAR] are taken in vertical axes. FIG.2A shows the optical performance of the astigmatic lens having adiameter of 80 [mm], and FIG. 2B shows the optical performance of theastigmatic lens having a diameter of 70 [mm]. In FIGS. 2A and 2B,central portions shown in reference letters C are respectively regionshaving a converted visual acuity value of 0.1 [logMAR] or below, andclear visual regions where objects are clearly seen. Absolute sizes ofclear visual regions C are identically set up in both lenses.

A method for displaying the optical performances of the presentinvention is applied to the astigmatic lenses described above.

First, rays enter from centers of rotation of the eyeballs to therespective astigmatic lenses with same intervals, and the number of raysB_(e) which transmit the entire astigmatic lenses and the number N whichtransmit the clear visual regions are measured. Measurement results arelisted in the following Table 2.

Subsequently, clear visual angles are calculated using theaforementioned equation (r), and simultaneously clear visual diametersare calculated by substituting the calculated results with theaforementioned equation (q).

Furthermore, for comparison, clear visual region ratios P% arecalculated using the aforementioned equation (n) as a method previouslydevised by the inventors. Respective calculation results are listed inTable 2.

TABLE 2 Clear visual Clear visual B_(e) N P % angle diameter Diameter 802493 1567 63% 89 degrees 56 mm Diameter 70 2165 1567 72% 89 degrees 56mm

As shown in Table 2, values of the clear visual angles and values of theclear visual diameters are respectively expressed as concrete numericalvalues. Therefore, when they are compared on seeing longitudinalaberration graphs or the like, the optical performances of a singlespectacle lens are quantitatively and easily evaluated. Furthermore, thevalues of the clear visual angles are expressed by a unit of degree [°],and the values of the clear visual diameters are expressed by a unit of[mm]; therefore, even those who do not have technical knowledge caninstinctively and easily understand a meaning of these numerical values.Furthermore, the optical performances of an axially asymmetric lens suchas an astigmatic lens can be quantitatively evaluated as an entire lens.

Incidentally, an expression by the clear visual region ratio P% is easyto understand; however, the clear visual region ratio P% changes when alens diameter changes as shown in Table 2. In other words, when theclear visual regions are identical, a value of the clear visual regionratio P% increases because a ratio of the clear visual region becomesrelatively larger as the lens diameter becomes small. Accordingly,spectacle lenses having different diameters are hard to evaluate from aview of an absolute size of the clear visual region.

In contrast to the above, the values of the clear visual angles and theclear visual diameters according to the aforementioned display methodare identical in both lenses. This shows that the sizes of the clearvisual regions respectively having different diameters can be justlyevaluated. In other words, according to the display method of thepresent invention, a comparison of the optical performances of thelenses having different design conditions such as the diameter or thelike can be appropriately and easily conducted.

EXAMPLE 2

Optical performances of two astigmatic lenses respectively havingdiameters of 80 [mm] and 60 [mm] are calculated. Common lens data or thelike of both are the same as Example 1. FIG. 3 is a viewthree-dimensionally displaying the optical performances of the lensesfor explaining clear visual regions in the astigmatic lenses as well asFIG. 2. FIG. 3A shows the optical performances of the astigmatic lenshaving a diameter of 80 [mm], and FIG. 3B shows the optical performancesof the astigmatic lens having a diameter of 60 [mm]. In FIGS. 3A and 3B,central portions shown in reference letters C are respectively regionshaving a converted visual acuity value of 0.1 [logMAR] or below, andclear visual regions where objects are clearly seen. Absolute sizes ofclear visual regions C are identically set up in both lenses.

A method for displaying the optical performances of the presentinvention is applied to the astigmatic lenses described above.

First, rays enter from centers of rotation of the eyeballs to therespective astigmatic lenses with same intervals, and the number of raysB_(e) which transmit the whole astigmatic lenses and the number N whichtransmit the clear visual regions are measured. Measurement results arelisted in the following Table 3.

Subsequently, clear visual angles are calculated using theaforementioned equation (r), and simultaneously clear visual diametersare calculated by substituting the calculated results with theaforementioned equation (s).

Furthermore, for comparison, clear visual region ratios P% arecalculated using the aforementioned equation (n) as a method previouslydevised by the inventors. Respective calculation results are listed inTable 3.

TABLE 3 Clear visual Clear visual B_(e) N P % angle diameter Diameter 802493 1567 63% 89 degrees 56 mm Diameter 60 1801 1499 83% 87 degrees 54mm

The clear visual region ratio P% changes when a lens diameter changes asshown in Table 3. A difference in both diameters is 20 [mm], and theclear visual region ratio P% changes larger than that in Example 1.

In contrast to the above, the values of the clear visual angles and theclear visual diameters according to the present invention are almostsimilar in both lenses.

It should be noted that a reason why the clear visual angles and theclear visual diameters slightly change according to the respective lensdiameters is thought that the clear visual angles and the clear visualdiameters are respectively underestimated because a part of an outsidediameter in a circumferential edge of the astigmatic lens having adiameter of 60 [mm] is not included in the lens diameter as the clearvisual region on calculating a solid angle.

However, to a phenomenon that the clear visual region ratio P% largelychanges when a diameter changes, as described above, a ratio of changeof the clear visual angle and the clear visual diameter is so littlethat the lenses can be used with no practical problem.

INDUSTRIAL APPLICABILITY

According to the present invention, a method for displaying opticalperformances preferably applicable to also an axially asymmetricspectacle lens is provided. Furthermore, according to the presentinvention, a comparison of the optical performances of the lenses havingdifferent design conditions such as a diameter or the like isappropriately and easily conducted. Furthermore, according to thepresent invention, the optical performances as the entire lens can bequantitatively evaluated. Furthermore, according to the presentinvention, the optical performances of the spectacle lens can bedisplayed instinctively and easily to understand.

1. A method for displaying the optical performance of a spectacle lens,comprising: determining a clear visual region of the spectacle lens;calculating a solid angle from the clear visual region and a center ofrotation of an eye; assuming a spherical cone which has an equal solidangle with the solid angle thus calculated and is symmetrical to anoptical axis of said spectacle lens; calculating an optical performancevalue which depends on a size of the clear visual region, based on thestep of assuming the spherical cone; and displaying the opticalperformance of the spectacle lens using the calculated opticalperformance value.
 2. The method for displaying the optical performanceof the spectacle lens according to claim 1, wherein said calculation ofthe optical performance value includes calculating a value of a clearvisual angle corresponding to a vertex angle of the spherical cone. 3.The method for displaying the optical performance of the spectacle lensaccording to claim 2, wherein the clear visual angle is calculated usingthe following equation (1) on the calculation of the clear visual angle:$\begin{matrix}\left\lbrack {{Equation}\mspace{14mu} 1} \right\rbrack & \; \\{{{first}\mspace{14mu}{clear}\mspace{14mu}{visual}\mspace{14mu}{angle}} = {\lim\limits_{K\rightarrow\infty}{2 \times {\cos^{- 1}\left( {1 - \frac{Ad}{K}} \right)}}}} & (1)\end{matrix}$ where, K is the number of incident rays when many rays arerandomly made incident to a front hemisphere of the spectacle lens, andAd is the number of transmitted rays which transmit the clear visualregion out of the incident rays.
 4. The method for displaying theoptical performance of the spectacle lens according to claim 2, whereinthe clear visual angle is approximately calculated by using thefollowing equation (2) on the calculation of the clear visual angle:$\begin{matrix}\left\lbrack {{Equation}\mspace{14mu} 2} \right\rbrack & \; \\{{{second}\mspace{14mu}{clear}\mspace{14mu}{visual}\mspace{14mu}{angle}} \cong {2 \times L \times \sqrt{\frac{N}{\pi}}}} & (2)\end{matrix}$ where, L is a degree interval when many rays enter fromthe center of rotation of the eye to the spectacle lens with a samedegree interval, and N is the number of the rays which transmit theclear visual region among incident rays.
 5. The method for displayingthe optical performance of the spectacle lens according to claim 2,wherein the calculated value of the clear visual angle by thecalculation of the clear visual angle is expressed by a unit of degreeas the optical performance value on said display of the opticalperformance of the spectacle lens.
 6. The method for displaying theoptical performance of the spectacle lens according to claim 1, whereinthe spherical cone has a center of rotation of the eye as a vertex andhas a spherical portion on a side of the spectacle lens; and saidcalculation of the optical performance value includes calculating avalue of a clear visual diameter corresponding to a diameter of acircle, the circle representing a part where the surface obtained byextending the side surface of the spherical cone and a flat surfacewhich is perpendicular to the optical axis and which includes a rearvertex of the spectacle lens cross.
 7. The method for displaying theoptical performance of the spectacle lens according to claim 2, whereinsaid calculation of the optical performance value further includescalculating a clear visual diameter by substituting the calculated valueof the clear visual angle on the calculation of the clear visual anglewith the following equation (3). $\begin{matrix}\left\lbrack {{Equation}\mspace{14mu} 3} \right\rbrack & \; \\{{{clear}\mspace{14mu}{visual}\mspace{14mu}{diameter}} = {2 \times {VR} \times {\tan\left( \frac{{clear}\mspace{14mu}{visual}\mspace{14mu}{angle}}{2} \right)}}} & (3)\end{matrix}$ where, VR is a distance between the rear vertex of thespectacle lens and the center of rotation of the eye.
 8. The method fordisplaying the optical performance of the spectacle lens according toclaim 6, wherein the calculated value of the clear visual diameter bythe calculation of the clear visual diameter is expressed by a unit oflength as the optical performance value on said display of the opticalperformance of the spectacle lens.
 9. The method for displaying theoptical performance of the spectacle lens according to claim 1, whereinthe clear visual region of the spectacle lens is determined using anevaluation function about visual acuity of the spectacle lens on saiddetermination of the clear visual region.
 10. The method for displayingthe optical performance of the spectacle lens according to claim 9,wherein converted visual acuity is used as the evaluation function aboutvisual acuity.
 11. The method for displaying the optical performance ofthe spectacle lens according to claim 3, wherein the calculated value ofthe clear visual angle by the calculation of the clear visual angle isexpressed by a unit of degree as the optical performance value on saiddisplay of the optical performance of the spectacle lens.
 12. The methodfor displaying the optical performance of the spectacle lens accordingto claim 4, wherein the calculated value of the clear visual angle bythe calculation of the clear visual angle is expressed by a unit ofdegree as the optical performance value on said display of the opticalperformance of the spectacle lens.
 13. The method for displaying theoptical performance of the spectacle lens according to claim 3, whereinsaid calculation of the optical performance value further includescalculating a clear visual diameter by substituting the calculated valueof the clear visual angle on the calculation of the clear visual anglewith the following equation (3). $\begin{matrix}\left\lbrack {{Equation}\mspace{14mu} 3} \right\rbrack & \; \\{{{clear}\mspace{14mu}{visual}\mspace{14mu}{diameter}} = {2 \times {VR} \times {\tan\left( \frac{{clear}\mspace{14mu}{visual}\mspace{14mu}{angle}}{2} \right)}}} & (3)\end{matrix}$ where, VR is a distance between the rear vertex of thespectacle lens and the center of rotation of the eye.
 14. The method fordisplaying the optical performance of the spectacle lens according toclaim 4, wherein said calculation of the optical performance valuefurther includes calculating a clear visual diameter by substituting thecalculated value of the clear visual angle on the calculation of theclear visual angle with the following equation (3). $\begin{matrix}\left\lbrack {{Equation}\mspace{14mu} 3} \right\rbrack & \; \\{{{clear}\mspace{14mu}{visual}\mspace{14mu}{diameter}} = {2 \times {VR} \times {\tan\left( \frac{{clear}\mspace{14mu}{visual}\mspace{14mu}{angle}}{2} \right)}}} & (3)\end{matrix}$ where, VR is a distance between the rear vertex of thespectacle lens and the center of rotation of the eye.
 15. The method fordisplaying the optical performance of the spectacle lens according toclaim 7, wherein the calculated value of the clear visual diameter bythe calculation of the clear visual diameter is expressed by a unit oflength as the optical performance value on said display of the opticalperformance of the spectacle lens.
 16. The method for displaying theoptical performance of the spectacle lens according to claim 13, whereinthe calculated value of the clear visual diameter by the calculation ofthe clear visual diameter is expressed by a unit of length as theoptical performance value on said display of the optical performance ofthe spectacle lens.
 17. The method for displaying the opticalperformance of the spectacle lens according to claim 14, wherein thecalculated value of the clear visual diameter by the calculation of theclear visual diameter is expressed by a unit of length as the opticalperformance value on said display of the optical performance of thespectacle lens.
 18. The method for displaying the optical performance ofthe spectacle lens according to claim 2, wherein the clear visual regionof the spectacle lens is determined using an evaluation function aboutvisual acuity of the spectacle lens on said determination of the clearvisual region.
 19. The method for displaying the optical performance ofthe spectacle lens according to claim 3, wherein the clear visual regionof the spectacle lens is determined using an evaluation function aboutvisual acuity of the spectacle lens on said determination of the clearvisual region.
 20. The method for displaying the optical performance ofthe spectacle lens according to claim 4, wherein the clear visual regionof the spectacle lens is determined using an evaluation function aboutvisual acuity of the spectacle lens on said determination of the clearvisual region.
 21. The method for displaying the optical performance ofthe spectacle lens according to claim 5, wherein the clear visual regionof the spectacle lens is determined using an evaluation function aboutvisual acuity of the spectacle lens on said determination of the clearvisual region.
 22. The method for displaying the optical performance ofthe spectacle lens according to claim 6, wherein the clear visual regionof the spectacle lens is determined using an evaluation function aboutvisual acuity of the spectacle lens on said determination of the clearvisual region.
 23. The method for displaying the optical performance ofthe spectacle lens according to claim 7, wherein the clear visual regionof the spectacle lens is determined using an evaluation function aboutvisual acuity of the spectacle lens on said determination of the clearvisual region.
 24. The method for displaying the optical performance ofthe spectacle lens according to claim 11, wherein the clear visualregion of the spectacle lens is determined using an evaluation functionabout visual acuity of the spectacle lens on said determination of theclear visual region.
 25. The method for displaying the opticalperformance of the spectacle lens according to claim 12, wherein theclear visual region of the spectacle lens is determined using anevaluation function about visual acuity of the spectacle lens on saiddetermination of the clear visual region.
 26. The method for displayingthe optical performance of the spectacle lens according to claim 13,wherein the clear visual region of the spectacle lens is determinedusing an evaluation function about visual acuity of the spectacle lenson said determination of the clear visual region.
 27. The method fordisplaying the optical performance of the spectacle lens according toclaim 14, wherein the clear visual region of the spectacle lens isdetermined using an evaluation function about visual acuity of thespectacle lens on said determination of the clear visual region.
 28. Themethod for displaying the optical performance of the spectacle lensaccording to claim 18, wherein converted visual acuity is used as theevaluation function about visual acuity.
 29. The method for displayingthe optical performance of the spectacle lens according to claim 19,wherein converted visual acuity is used as the evaluation function aboutvisual acuity.
 30. The method for displaying the optical performance ofthe spectacle lens according to claim 20, wherein converted visualacuity is used as the evaluation function about visual acuity.
 31. Themethod for displaying the optical performance of the spectacle lensaccording to claim 21, wherein converted visual acuity is used as theevaluation function about visual acuity.
 32. The method for displayingthe optical performance of the spectacle lens according to claim 22,wherein converted visual acuity is used as the evaluation function aboutvisual acuity.
 33. The method for displaying the optical performance ofthe spectacle lens according to claim 23, wherein converted visualacuity is used as the evaluation function about visual acuity.
 34. Themethod for displaying the optical performance of the spectacle lensaccording to claim 24, wherein converted visual acuity is used as theevaluation function about visual acuity.
 35. The method for displayingthe optical performance of the spectacle lens according to claim 25,wherein converted visual acuity is used as the evaluation function aboutvisual acuity.
 36. The method for displaying the optical performance ofthe spectacle lens according to claim 26, wherein converted visualacuity is used as the evaluation function about visual acuity.
 37. Themethod for displaying the optical performance of the spectacle lensaccording to claim 27, wherein converted visual acuity is used as theevaluation function about visual acuity.